Thermal Analysis of Apparatus having Multiple Thermal Control Zones

ABSTRACT

Systems and methods for conducting thermal analysis in materials and devices having multiple thermal control zones are provided. Modem apparatuses, such as manifolds, generally have several thermal devices that introduce or remove heat at different rates from several different regions. Previous attempts to determine a thermal profile required constant guessing and an unknown number of simulations to arrive at an acceptable result. Further, since the number of simulations required is not known from the onset of the operation, the duration is unknown, which is often unsatisfactory to manufacturing personnel. Disclosed embodiments include the use of FEA to aid in designing and/or evaluating manifold systems. In one embodiment, finite element analysis is conducted to determine the heat flux caused upon other control zone by a thermal device in a specified control zone.

INTRODUCTION

This invention relates to systems, methods and devices for conductingthermal determinations of apparatus, such as design or analysis ofapparatus or devices. More specifically, aspects of the invention aredirected towards thermal design or analysis of apparatus or deviceshaving multiple thermal control zones.

BACKGROUND

Industrial tools and other apparatus are often placed under high stressloads. The stress may be in the form of, for example, mechanical,frictional, and/or extreme thermal conditions. This is especially trueof tools utilized in manufacturing products under high temperatures andpressures, such as tools for making injection molded plastic products.Such tools must not only be designed to withstand the thermalconditions, but also to remain within certain pre-defined operatingthermal parameters for proper operation. For example, when injectionmolding resin or other materials to create plastic products, utilizing atemperature that is too high could result in “burning” the resin and/orimproper formation of the desired product. Conversely, if a desiredtemperature is not reached, the resins may not properly flow or mix orotherwise perform suitably to form the desired end-product. The complexproblem of properly designing apparatus such as industrial tools iscompounded when the apparatus has multiple thermal zones, eachcomprising one or more thermal devices, such as heaters or coolers, thataffect temperature in their own zone and that of other zones of theapparatus.

Modern apparatus, for example injection molding manifolds and the like,generally have more than one thermal device, each of which, as explainedin more detail below, introduces or removes heat from the apparatus.Generally, each region or zone of the apparatus is in thermalcommunication with one or more other zones of the apparatus. Thusdesigning and analyzing the thermal properties or performance of suchapparatus, including, for example, determining a thermal profile of theapparatus under usage conditions, requires recognition that each zoneimpacts the thermal properties or performance of one or more otherzones. As one skilled in the art will readily appreciate, this is acomplex and time consuming undertaking, especially with an apparatushaving multiple thermal control zones, where each zone has a controlassociated with a thermal device whose thermal output affects thethermal properties or performance of one or more of the other controlzones, each of which may, in turn, have a control and an associatedthermal device that influences the thermal properties or performance ofthe first and/or other control zones of the apparatus.

Previous approaches used to determine a thermal profile of an apparatusincluded the use of an iterative process employing finite elementanalysis (FEA). Typically, in such prior approaches, a large number ofcalculation simulations are needed to approach an estimation of thethermal profile of the apparatus in operation. Such simulations requireundesirably large amounts of computing and personnel time. Alsounfortunately, such known iterative processes require guessing orestimating the value of one or more variables and an unknown number ofsimulations to arrive at an acceptably accurate result. The requiredcomputational time for each successive simulation to be performed oftenprecludes the computation of a fully satisfactory estimate of thethermal profile of the apparatus. Rather the process is often stopped orotherwise not conducted before a more precise and accurate result isobtained. Further, since the number of simulations required is not knownfrom the onset of the operation, the duration is unknown, which is oftenunsatisfactory to manufacturing personnel. Where each of multiple zonesof an apparatus has a thermal device whose thermal output indirectlyaffects the thermal properties of one or more of the other controlzones, the synergistic complexity of the problem increases as the numberof control zones increases.

Some or all of these and other shortcomings of traditional methods ofdetermining a thermal profile of an apparatus having a plurality ofthermal control zones are overcome according to various methods andsystems encompassed in different embodiments of the invention.Additional objects or advantages of various embodiments of the inventionwill be apparent from the following disclosure.

SUMMARY

A first aspect of the invention is directed towards methods and systemsimplementing finite element analysis to aid in the determination, e.g.,the design or analysis, of an apparatus having multiple thermal controlzones. In certain exemplary embodiments the methods and systems arefixed-simulation methods and systems, as further disclosed below. Incertain exemplary embodiments, the apparatus has multiple thermalcontrol zones, each of which control zones has a control (also referredto here as a thermal controller) and an associated thermal device, suchas a heater or cooler, whose thermal output directly affects the thermalperformance or properties (e.g., the temperature) of that zone and alsodirectly or indirectly affects the thermal properties of one or more ofthe other control zones of the apparatus. In certain exemplaryembodiments, the apparatus to be designed or analyzed is a manifold forinjection molding plastic or other material, wherein the manifold hasmultiple thermal control zones, each of which control zones has acontrol and an associated thermal device whose thermal output directlyaffects the temperature of that zone and indirectly affects thetemperature of one or more of the other control zones of the manifold.

It will be understood by those skilled in the art, given the benefit ofthis disclosure, that the thermal device of any such zone of theapparatus may comprise operative components at one or more locations inthe zone. In addition, the boundary between one thermal control zone andthe next within an apparatus may in some instances be selected fromamongst multiple (even infinite) suitable alternatives. As one skilledin the art will readily appreciate upon reading the disclosure herein,the term boundary does not signify a physical separation or boarder(although in select embodiments, the boundary will be defined by aphysical structure). Rather, the boundary may be virtual and definedmerely on non-physical features. In select embodiments, the apparatus isdivided up into several symmetric portions. As used herein, theboundaries between control zones may be any line, collection of lines,plane or collection of planes defining at least a portion of border of aspecific control zone.

Typically, but not necessarily in all embodiments disclosed here, athermal zone of a multi-zone apparatus designed or analyzed by a finiteelement analysis method or system disclosed here is not controlled bythe thermal controller of another zone other than indirectly, such as bythe cross-boundary effect of the temperature of one zone on adjoiningzones. It will be within the ability of those skilled in the art, giventhe benefit of this disclosure, to determine suitable zone boundaries.

In accordance with another aspect, certain systems and methods disclosedhere employ a finite element analysis to determine, i.e., to design orto analyze the design of apparatus (i.e., within all or at least aportion of the body of the apparatus or of components of the apparatus)having multiple, independently controlled thermal control zones, whereinthe temperature of at least one such zone during operation of theapparatus directly or indirectly affects the temperature of at least oneother such zone. As the term is used here, zones are “independentlycontrolled” if (i) the thermal device(s) within the zone are actuated(e.g., operated or energized) only in response (directly or indirectly)to signals generated by one or more temperature sensors within that zoneand/or (ii) the thermal device(s) within the zone are not adapted to beactuated in response (directly or indirectly) to signals generated byany temperature sensor(s) within any other zone of the zone.

In certain exemplary embodiments finite element analysis is implementedto aid in the design or analysis of a manifold system, e.g., aninjection molding manifold system, comprising one or more than oneindividual manifold. In certain embodiments, for example,fixed-simulation finite element analysis is conducted to determine theheat flux caused by actuation of a thermal device in a specified controlzone of the manifold system upon one or more other control zones of themanifold system. In certain such embodiments, the thermal device of acontrol zone is a heater, such as but not limited to resistive heater.In certain exemplary embodiments the heater is operative to heat aliquid or other fluid in a channel extending in the manifold, includingat least partially in the particular control zone in question. Yet inother embodiments, the heater is operative to maintain an elevatedtemperature of a liquid or other fluid in the manifold. As used herein,the term liquid may include any chemical, matter or material that maychange shape as it travels through a passage, such as a channel. Forexample, the liquid may be fine or course, and at select temperatures beconsidered a semi-solid. The texture of the liquid may range from denseto soft and from runny to a paste-like consistency including slurries.Thus, in select embodiments, the liquid forms to the shape of thepassage it is traveling within.

In certain exemplary embodiments the thermal device of a control zone isa cooler or chiller, e.g., a thermoelectric cooling device operative toremove heat from the zone in question. Other embodiments of theinvention will be readily apparent to those of ordinary skill in theart, including, e.g., embodiments wherein finite element thermalanalysis as disclosed here is used to determine other thermalparameters. As used here, the term thermal parameters is used to meanthe thermal operating properties, thermal performance under normaloperating conditions or under other conditions, thermal profile(temperature gradients or the like) and/or other properties,characteristics, etc. of an injection molding manifold or otherapparatus having multiple thermal control zones.

In accordance with another aspect, systems and methods compriseimplementation of finite element thermal analysis to determine thethermal parameters of an apparatus having multiple control zones, andfurther comprises utilizing the results of such analysis, e.g., thethermal relationship between zones of the apparatus obtained from suchfinite element analysis to determine a thermal profile of the apparatusunder defined conditions. In certain exemplary embodiments, the thermalprofile graphically displays the temperature values obtained, e.g., byone or more graphical displays visible to a user. In furtherembodiments, the thermal profile may be utilized to further aid in thedesign of the apparatus, e.g., determining an initial design for theapparatus before it is constructed or determining an alteration of theexisting design of the apparatus.

In accordance with another aspect of the invention, finite elementanalysis is utilized in a system or method to create an influence matrixsuitable for use in determining the design of an apparatus, e.g., to aidin the confirmation of a thermal profile of an injection moldingmanifold or other apparatus having multiple control zones. In certainexemplary embodiments, one control zone may span over multiplecomponents.

In certain exemplary embodiments finite element thermal analysis isemployed to determine the thermal profile of a defectively operatingapparatus having multiple control zones, e.g., an injection moldingmanifold, and the thermal profile is used in determining why theapparatus is operating defectively, e.g., not operating optimally oreffectively or according to expectations or specifications or otherwisemalfunctioning. In certain such embodiments, the results of suchdetermination are utilized to determine a design change or other stepsto correct the deficiency. One skilled in the art will readilyappreciate that one or more of the steps or features of the methods andsystems disclosed here may be carried out by computer-executableinstructions stored on one or more computer-readable mediums.

Those of ordinary skill in the art will recognize and understand fromthis disclosure and the further discussion below, various alternativeand optional additional features and advantages of the methods andsystems disclosed here for implementing finite element analysis in thedesign or analysis of apparatus having multiple thermal control zones.Also, additional aspects and advantages of the present invention will beapparent to those skilled in the art from the following detaileddescription of certain embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The following detailed discussion of certain select embodiments willrefer to the appended drawings in which:

FIG. 1 is a flowchart of an exemplary finite element analysis method orsystem according to one aspect of the invention, for determining thethermal profile of an apparatus having multiple thermal control zones.

FIG. 2 a shows a perspective view of an exemplary model of amulti-component injection molding manifold having multiple thermalcontrol zones, which may be analyzed by a finite element analysis methodor system according to certain exemplary embodiments of the invention.

FIG. 2 b is a perspective view of an exemplary modeled portion of amanifold having multiple thermal control zones, which may be analyzed bya finite element analysis method or system according to certainexemplary embodiments of the invention.

FIG. 3 a is an exemplary thermal matrix providing exemplary data toillustrate a finite element analysis method or system according tocertain exemplary embodiments of the invention.

FIG. 3 b is an exemplary temperature matrix of a manifold having threecontrol zones, providing exemplary data to illustrate a finite elementanalysis method or system according to certain exemplary embodiments ofthe invention.

FIG. 4 is a perspective view of an exemplary thermal profile of aportion of a manifold system having more than one control zone,utilizing the data shown in FIG. 3 b.

DETAILED DESCRIPTON OF CERTAIN EXEMPLARY EMBODIMENTS

The exemplary methods and systems herein are further disclosed anddescribed below in the context of industrial injection molding manifoldsfor ease of understanding only, however, one skilled in the art willreadily understand that other applications, industrial or otherwise, arewithin the scope of the invention. Thus, the finite element methods andsystems of the present disclosure are useful in analyzing or designingany apparatus having multiple thermal control zones. As used here, theterm apparatus is used broadly to mean apparatus, devices, assemblies,sub-assemblies and the like.

FIG. 1 is an exemplary flowchart of a method of analyzing the design ofa manifold according to one aspect of the invention. The applicabilityof FIG. 1 and the description below to system embodiments of the presentinvention will be readily apparent to those of ordinary skill in the artgiven the benefit of this disclosure. As one skilled in the art willreadily appreciate, the method may be modified to include fewer oradditional steps according to various embodiments of the invention. Themethod of FIG. 1 can be utilized to determine the design of a manifold,e.g., to develop a suitable design for a manifold. Further, the methodmay be utilized to analyze the design of an existing manifold, e.g., todevelop a thermal profile comprising estimated temperature gradientswithin the manifold under a defined set of conditions, e.g. under themanifold's normal operating conditions. The method may also be modifiedaccording to the teachings of this disclosure to redesign an existingmanifold. This would be particularly advantageous when an existingmanifold is not operating properly or efficiently. For example,scorching or improper flow of injection molding material may be due totemperatures in one or more of the zones of the manifold (at some or alltimes during the injection molding cycle) which are too high or too low.Adjusting the thermal controller for that zone may or may not besuitable or sufficient to correct the problem. For example, adjustingthe thermal controller for that zone may not be suitable or sufficientif it is being adversely affected by the thermal properties (e.g., thetemperature) of one or more of the other control zones. One or moremethods as disclosed and described here may be utilized to determine thesource of the problem, provide a result to suggest a particular retrofitor adjustment to remedy the problem, and/or aid in the design of such aretrofit. Such adjustment may, for example, be in the design of themanifold and/or in the manner in which it is operated, including, e.g.,the temperature set points of the zone controllers, etc.

At exemplary step 102 of FIG. 1, a model of an apparatus, such as amanifold system, having a plurality of thermal control zones isreceived. As used herein, each thermal control zone of the manifold hasat least one thermal input and at least one thermal output. According toone embodiment of the invention, each thermal control zone comprises athermal controller and a thermal device. The thermal controllertypically is configured to transmit a control signal (or not transmitsuch a signal), in response to a thermal parameter at a specificlocation within the manifold, e.g., a thermocouple or other temperaturesensor adapted to transmit or not transmit a signal in response to thetemperature of the manifold at the location of the sensor in the zone inquestion being below or above a set point. The signal may be transmittedby the sensor directly to the thermal device, i.e., to the thermaldevice or to an associated microprocessor or the like or other circuitryto cause ultimately a corresponding actuation or de-actuation of thethermal device. It should be understood in this regard that, while asingle microprocessor or the like or other circuitry may be used toreceive and process control signals from the sensors or othercontrollers of multiple zones, the control signal from the thermalcontroller of a particular zone is the sole or primary control signalfor the thermal device(s) of that particular control zone. As usedherein, a thermal device for a zone may be any device operative underthe control of the associated controller to heat or cool the zone, forexample, an electric, fluidic or other heater, thermoelectric cooler,heat sink, heat pipe, or any combination thereof. In essence anycomponent or group of components that is intentionally configured toprovide or remove thermal energy from the control zone may be a thermaldevice.

As used herein, an apparatus or system may comprise one or morecomponents that are in thermal communication with each other. FIG. 2 ashows an exemplary model of multi-component manifold that may beemployed according to one implementation of step 102 of FIG. 1. Manifoldsystem 200 includes manifold 202 and manifold 204 which, in turn, can beconceptually divided into multiple thermal control zones for analysis inaccordance with the methods and systems disclosed here. Each of themultiple thermal control zones has a thermal controller and anassociated thermal device. As shown, manifold 202 includes thermaldevice 206 and thermal controller 208.

The model of manifold system 200 may be configured such that thermalcontroller 208 detects, measures, receives or otherwise determines athermal parameter of or corresponding to its thermal zone, such as thetemperature of the manifold at thermal controller 208 or the temperatureof resin or other molding material fed through channel 210 of themanifold to molding cavities. In certain other exemplary embodiments,multiple thermal controllers may be utilized in a thermal control zoneto detect, measure, receive or otherwise determine the thermalparameter(s) at multiple locations within the zone. The control signalsfrom such multiple controllers may be used collectively (e.g., withaveraging or other combination or selective elimination, etc.),serially, or otherwise to control the heater or other thermal device ofthe zone.

Other thermal parameters, i.e., other determinable values or parameterscorresponding to the temperature or other suitable thermal property ofthe zone, may be utilized, such as but not limited to conduction,convection, radiation, and/or internal heat generation. In response tothe thermal parameter at a specific location within the apparatus,thermal controller 208 is configured to transmit a control signaldirectly or indirectly to thermal device 206 located within the samecontrol zone as thermal controller 208. As noted above, the controlsignal may be fed directly to the thermal controller or may utilize anindirect connection, such as via a microprocessor or the like. As willbe appreciated by those skilled in the art, such a process may be partlyor wholly implemented through the use of computer-executableinstructions stored on one or more computer-readable mediums that are inelectronic communication with one or more such processors.

Thermal device 206 and any associated circuitry, devices or the like,including, e.g., electrical power feed means, etc., is operable inresponse to the control signals from (directly or indirectly, asdiscussed above) associated thermal controller 208. The control signalmay, e.g., alter the operating state of thermal device 206, such asincreasing or reducing the power supplied to thermal device 206,initiating, terminating or otherwise adjusting the flow of heating orcooling fluid to or through thermal device 206, etc. For example, if thethermal device is a heater, reducing the power may reduce the heatemitted by thermal device 206. In other embodiments, the control signalmay merely switch the power state of thermal device 206 between an “ON”state and an “OFF” state.

Returning to FIG. 2 a, manifold 204 comprises thermal device 212 that isassociated with thermal controller 214 and thermal device 216 that isassociated with thermal controller 218. Therefore, manifold 204comprises at least two thermal control zones or at least a portion ofeach of at least two control zones. As seen in FIG. 2 a, portions ofmanifold 202 are in close proximity to thermal device 212 and thermalcontroller 214 of manifold 204. In fact, location 220 of manifold 204 isproximate to portions of manifold 202. Therefore, in one embodiment,portions of manifold 202 may be considered in the same control zone asportions of 204. Alternatively, the manifold system can be divided intoa different set of thermal control zones. In select embodiments, thethermal control zones are symmetric with respect to each other, whereasin other embodiments, the control zones are determined by a myriad offactors. It will be within the ability of those of ordinary skill in theart, given the benefit of this disclosure, to suitably divide a manifoldor other apparatus into multiple control zones for design or analysis inaccordance with the finite element methods disclosed here.

Also located on manifold 204 of model 200 is thermal device 216 andthermal controller 218, which both belong to the same control zone,specifically, a control zone different from that of thermal device 212and thermal controller 214. In addition to being primarily thermallycontrolled by its own thermal device and thermal controller, thetemperature and/or other thermal properties or performance of each suchcontrol zones are affected by the inputs of the thermal device of theother control zone as well as possibly the inputs of thermal device 206.

As shown, model 200 is in graphical form, however, one skilled in theart, given the benefit of this disclosure, will readily appreciate thatthe model and any information relating to the model provided in step 102may be in any form, including graphical, numerical, binary, andcombinations thereof so long as the model includes or represents or isbased on or otherwise incorporates at least one aspect of the physicalgeometry of the system which it represents. The received data mayrepresent a 2-dimensional model or a more complex 3-dimensional model.

Returning to FIG. 1, at least one input regarding at least one materialof the apparatus or system represented by the model utilized in step 102(such as model 200), is provided in step 104. The input may be a manualuser-input providing information regarding one or more materials,chemicals or compositions utilized or intended to be utilized to makethe physical system. The information may, for example, be one or morephysical or performance properties, e.g., thermal conductivity, heatcapacity or thermal capacitance, specific heat capacity (also calledmore properly “mass-specific heat capacity” or more loosely “specificheat”), boundary conditions, or the like, etc. In one embodiment wherethe model is directed towards a system that is already designed, thematerials may be detected by automated mechanisms or automaticallysubmitted to the model. In still yet further embodiments, the input isprovided as part of step 102. The input may be in any suitable form,e.g., textual, numerical, binary or combinations thereof, and optionallyis converted to another form for use within the process.

The input may be the value of a single physical or performance propertyor a value representing multiple physical or performance properties inany suitable combination. Multiple inputs may be received regarding thesame material, such as the material's composition, heat capacity,specific heat capacity, thermal conductivity, density, strength, etc. Inother exemplary embodiments, only one input is received and may then beassociated with several qualities of the material, e.g., qualities thatare stored on a computer-readable medium. In yet other exemplaryembodiments, one or more inputs are received for multiple materials thatmake up the apparatus or system. For example, manifold 202 of model 200may comprise one or more materials not included in manifold 204, andinputs may be received for each.

In step 106, a mesh for the model, such as model 200 is defined. Asreadily known to those skilled in the art, a plurality of nodes aremapped or otherwise distributed around the modeled topography of thesystem or select areas of the system of interest. The nodes areinterconnecting, wherein each node is modeled to be in communicationwith and to be affected by any changes to at least one other node it isin communication with. The quantity, distribution, and density of thenodes for any given determination (i.e., analysis or design) inaccordance with the methods and systems disclosed here may be determinedby those of ordinary skill in the art given the benefit of thisdisclosure, based on factors, including but not limited to, the desiredaccuracy of the result, geometry of one or more components of theapparatus being analyzed, the material(s) used in the apparatus or itscomponent(s), the design of the apparatus or system, and/or other areasof specific concern applicable to the particular analysis. In certainexemplary embodiments, each control zone is represented by a fixednumber of nodes ranging from 1 to a maximum quantity, yet in otherembodiments, different quantities of nodes are assigned to variouscontrol zones based upon one or more factors, such as those describedabove. In certain exemplary embodiments, the mesh is createdautomatically by computer-executable instructions stored on acomputer-readable medium. In certain such embodiments, manualmanipulation may be conducted to further refine the mesh. Those skilledin the art, given the benefit of this disclosure, will be well able toimplement suitable procedures for defining and manipulating a mesh asused herein.

FIG. 2 b shows a perspective view of a portion of exemplary model of amanifold that may be utilized according to select embodiments of theinvention. As shown, the exemplary portion of model 250 comprises a mesh252 that, when viewed graphically, appears similar to a net orspider-web that covers the outer surface of the model 250. The mesh 252divides the model 250 into discrete elements that are allinterconnected, with proximate nodes being in contact with neighboringnodes. As presented in the exemplary example, the nodes are notnecessarily symmetrically spaced, and have different shaped boundaries.As further seen with exemplary mesh 252, some elements may be largerthan others elements in addition to having different shapes.

In step 108, one or more factors relating to boundary conditions may beintroduced into process. As used herein, boundary conditions mayencompass or include any known parameters that introduce, remove, alter,and/or affect the distribution of a thermal parameter in the system. Forexample, the specific location of a nearby conductive manifold or othermechanism that affects a temperature condition may be inputted into thesystem to compensate for any heat loss due to the conductive manifold.As used throughout the specification, the term heat loss may encompass apositive or negative value to indicate a gain of heat energy or the lossof heat energy. Also, the outer boundaries of the manifold may beexposed to ambient air temperatures at one location while exposed toextreme temperatures at another, such as being in close proximity toanother manifold or section of the system that is known to affect one ormore temperature parameters.

Yet in another embodiment, a specific protrusion or attached component,made of the same or a different material as one or more manifolds, mayaffect one or more temperature parameters. For example, looking to FIG.2 a, contact plate 226 is operatively attached to manifold 202. In oneembodiment, the heat lost by contact plate 226 is readily known or maybe estimated and therefore may be provided to the system as an input asa known boundary condition. As one skilled in the art will readilyappreciate given the disclosure provided herein, according to oneembodiment, one or more boundary conditions may initially be an unknownfactor that may be calculated according to the teachings of selectaspects of the invention. For example, in one embodiment, a temperatureparameter of several control zones may be known in a manifold that hasalready been designed and/or manufactured. However, it would bedesirable to determine the effect of a boundary condition, such as theaddition of contact plate 226, may have upon the system. As demonstratedfrom the foregoing, there may be a plurality of boundary conditions thatmay differ across different portions of one or more components of anapparatus. As would be further appreciated by one skilled in the art,one or more boundary conditions may be considered in step 104, when thematerial data is provided.

In step 110, the determination of thermal correlation between aplurality of zones is initiated. One exemplary method of determining thethermal correlation is shown by way of the illustrative thermalinfluence matrix of FIG. 3 a. The exemplary thermal matrix 300 is formedby an [n×n] matrix, wherein “n” equals the number of control zones.Exemplary thermal matrix 300 provides exemplary data to illustrate oneprocess according to these aspects of the invention. As seen with column302, a fixed simulation process is conducted. The term fixed simulationsignifies that the number of simulations performed is equal to thenumber of thermal control zones (n=# of simulations). Columns 304, 306and 308 represent the specific control zones Htr_1, Htr_2, and Htr_3,respectively, which for example, may represent heaters 206, 212, and 216shown in FIG. 2 a. As discussed above, however, the control zones may beany set of areas that each has at least one thermal input and at leastone thermal output. The thermal input for a given zone may be, forexample, a value corresponding or correlating to the rate of heat lossfrom that zone under operating conditions at a given temperature, e.g.,at the temperature set point of the thermal controller of the zone inquestion. In a typical application, therefore, the temperature may, forexample, be the temperature at that zone's thermal controller,recognizing that a temperature gradient may exist in the zone from thelocation of the thermal controller to any other location in the zone.The thermal input for a given zone may be, for example, a valuecorresponding or correlating to the rate of heat input into that zone bythe thermal device of that zone, upon actuation, under operatingconditions.

The thermal relationship between each zone may be quantified by applyingan arbitrary value for a thermal parameter to one particular zone, whilethe other zones are unaltered. For each simulation, which will be equalto the number of control zones tested, the arbitrary value will remainthe same. For example, looking to simulation 1, designated by row 310,value “q” is applied to control zone Htr_1 while the two other exemplarycontrol zones remain unaltered. For simulation 2, designated by row 312,value “q” is applied to control zone Htr_2, while Htr_1 and Htr_3 areunaltered, and looking to simulation 3, designated by row 314, “q” isapplied to Htr_3 and the other two control zones are left unaltered.Thus, for each simulation, “q” is applied to a single control zone thatis different than the previous simulation, where the number ofsimulations equals the number of thermal control zones. In otherimplementations, another value that is different than “q” may beapplied, but the same value will be applied for each simulation, albeitat different control zones.

Columns 316, 318 and 320 provide the results for each control zone persimulation using the nomenclature Txy, where T designates a temperaturevalue is given, “x” designates the control zone for which T is beingmeasured and “y” designates the control zone that is causing theprovided value. For example, in Simulation #1 where “q” was only appliedto control zone 1 (Htr_1), the effect of “q” was measured for eachcontrol zone, including the zone for which it was applied. As seen incolumn 316, the value is T11, thus providing the temperature at controlzone 1 from the application of “q” at Htr_1. Column 318 for the samesimulation has a value T21, thus providing the temperature at controlzone 2 from the application of “q” at Htr_1 and column 310 has a valueof T31, thus providing the temperature at control zone 3 from theapplication of “q” at Htr_1. As predicted, for Simulation #2, the “y”will always be 2 and accordingly, will always be 3 for the Simulation#3.

Those skilled in the art will readily understand that any thermalparameters, such as those described in this application, as well asthose known in the art, may be utilized without departing from the scopeof the disclosure. To better acquaint the reader with a real-worldexample, FIG. 3 b is provided as an exemplary temperature matrix of amanifold having three control zones providing exemplary data toillustrate another process according to select embodiments of theinvention. As seen in FIG. 3 b, “q” is set to 0.1 W/mm², where “q” isthe arbitrary heat flux value corresponding to the heater for each ofthe three zones (during the 3 simulations). For each of the threesimulations, the temperature is recorded at each thermal controller'slocation (1 per control zone) and the influence matrix shown on theright side of FIG. 3 b may be calculated with the provided data, whereineach column provides the simulated temperature at each thermalcontroller due to the heat flux applied to the heater designated in thatparticular column.

Step 112 may then be implemented, where a thermal parameter for eachcontrol zone is applied. According to one embodiment, the thermalparameter is the temperature of a section of the manifold or fluidtraveling within the manifold at a specific location. For example, asshown in FIG. 2 a, thermal controller 208 may provide a temperaturevalue at its location. In other embodiments, thermal controller 208receives or measures the thermal parameter of a compound, such as aliquid in channel 210, as the liquid travels through a portion of thecontrol zone. One skilled in the art understands that any parameterrelating to a thermal property that is known regarding a plurality ofindividual control zones of interest may be utilized in step 112.

At step 114, the influence matrix may be utilized to obtain a result ofthe linear thermal relationship of an unknown thermal parameter for eachcontrol zone within the influence matrix. Using the manifold model 200of FIG. 2 a and influence matrix 300 of FIG. 3 as an example, in oneembodiment Equation (1) may be utilized to determine the steady-stateheat conduction with the three zones when the control zone input is atemperature, such as heat produced by thermal device 206, and thecontrol zone output is a heat flux (which is unknown)

Equation  (1):                                     T_(tc(1…3)) = {I_(temp)} × q_((1…3))

Looking to Equation 1, “T” is the temperature at the thermal controller,“q” is the heat flux, and “I” represents the influence matrix. In theexemplary embodiment, the input parameter “T” is known and provided fromstep 112, therefore, the equation is to be solved for the outputparameter “q”. Thus, in one embodiment, the equation may be used todetermine how much heat needs to come from a heater to get a certaintemperature at a thermal controller. As one skilled in the art willreadily appreciate, derivations of Equation 1 may be utilized to obtaina result of the linear thermal relationship of the unknown thermalparameters for each control zone within the influence matrix withoutdeparting from the scope of the recited aspects of the invention. In oneembodiment, FIG. 3 a may be utilized to determine output parameter “q”.

Equation  (2):                                      $\begin{Bmatrix}{q\; 1} \\{q\; 2} \\{q\; 3}\end{Bmatrix} = {\begin{bmatrix}{T\; 11} & {T\; 12} & {T\; 13} \\{T\; 21} & {T\; 22} & {T\; 23} \\{T\; 31} & {T\; 32} & {T\; 33}\end{bmatrix}^{- 1}\begin{Bmatrix}{{Tset} - {Tplate}} \\{{Tset} - {Tplate}} \\{{Tset} - {Tplate}}\end{Bmatrix}}$

Utilizing the “real-world data” presented in the exemplary influencematrix of FIG. 3 b, Equation 2 may be expressed as:

$\begin{Bmatrix}{q\; 1} \\{q\; 2} \\{q\; 3}\end{Bmatrix} = {\begin{bmatrix}680 & 684 & 293 \\255 & 846 & 636 \\63 & 232 & 1049\end{bmatrix}^{- 1}\begin{Bmatrix}{288 - 82} \\{288 - 82} \\{288 - 82}\end{Bmatrix}}$

where Tset=288 and Tplate=82, thus providing a result of:

$\begin{Bmatrix}{q\; 1} \\{q\; 2} \\{q\; 3}\end{Bmatrix} = {\begin{bmatrix}0.0163 \\0.0065 \\0.0172\end{bmatrix}{W/{mm}^{2}}}$

One skilled in the art will readily understand with aid of thisdisclosure derivations of Equation 2 that will adequately determine “q”or any other thermal value. For example, in one embodiment, {−Tplate}may be removed from the equation if delta T is not required or desired.In yet further embodiments, other components and computations may beadded to the equation being utilized to tailor the process for specificpurposes.

Once the thermal parameter, such as the heat flux is determined, step116 may then be applied to the FEA model to determine the thermalprofile of the system or portion of the system in question. For example,the heat flux obtained for each control zone may be applied to theheaters for the respective control zones in a finite element analysis tosimulate the correct thermal profile. FIG. 4 is a perspective view ofone exemplary thermal profile of a manifold system utilizing the datashown in FIG. 3 b. Yet in other embodiments, where a new system may bein the process of being designed, the profile obtained may be useful infurther development or design of the system, such as a multi-componentmanifold. Indeed, step 116 may be initiated to determine why a manifoldalready manufactured is not operating at optimal level or otherwisemalfunctioning. In one such embodiment, the results of step 116 may beutilized to determine how to fix the deficiency. For example, if onecontrol zone's thermal properties are adversely affecting the thermalproperties of another control zone, a thermal device may be added toremedy or fix the deficiency. In yet another embodiment, an existingthermal device may be altered to fix the deficiency.

The foregoing detailed description of preferred embodiments is intendedto be exemplary of the invention and illustrative. Modifications of theembodiments disclosed and alternative embodiments will be apparent tothose skilled in the art in view of the above, and all suchmodifications and alternatives are intended to be within the scope ofappropriate ones of the following claims. The appended claims areintended to cover all such modifications and alternative embodiments. Itshould be understood that the use of a singular indefinite or definitearticle (e.g., “a,” “an,” “the,” etc.) in this disclosure and in thefollowing claims follows the traditional approach in patents of meaning“at least one” unless in a particular instance it is clear from contextthat the term is intended in that particular instance to meanspecifically one and only one. Likewise, the term “comprising” is openended, not excluding additional items, features, and elements.

1. A method of determining a thermal parameter of an apparatus, themethod comprising: (a) providing a model of an apparatus having aplurality of thermal control zones, each thermal control zone of theapparatus comprising a thermal controller and a thermal device, whereinthe thermal controller of each thermal control zone is operative, inresponse to a thermal parameter at a location within that thermalcontrol zone, to generate a control signal directly or indirectly to thethermal device of that thermal control zone; (b) providing at least oneinput value that directly or indirectly corresponds to at least onethermal property of at least one material of the apparatus; (c) defininga finite element analysis mesh having nodes for the model of theapparatus; (d) applying at least one boundary condition value to atleast one portion of the model of the apparatus; (e) determining thethermal correlation among at least a selected plurality of the thermalcontrol zones, comprising constructing an [n×n] influence matrix ofmatrix values, where n equals the number of selected thermal controlzones, each matrix value corresponding to a value of a first thermalparameter selected from heat loss and temperature for a correspondingone of the thermal control zones, the constructing of the [n×n]influence matrix comprising conducting n finite element analysissimulations of the apparatus based on the finite element analysis mesh,the input value of (b) and the boundary condition value, each of the nfinite element analysis simulations comprising determining a matrixvalue of the first thermal parameter for each thermal control zone byapplying a value for the other thermal parameter selected from heat lossand temperature which is unknown to each boundary of a corresponding oneof the thermal control zones; and (f) using the finite element analysisinfluence matrix to determine the value of the second thermal parameterfor each control zone for a desired value of the first of the firstthermal parameter for each control zone included in the selectedplurality of thermal control zones.
 2. The method of claim 1, furthercomprising: (g) applying the result obtained in (f) to a finite elementanalysis simulation the model of (a) to obtain a thermal parameter forthe apparatus.
 3. The method of claim 1, further comprising: (g)applying the result obtained in (f) to an finite element analysissimulation the model of (a) to obtain a thermal profile for theapparatus.
 4. The method of claim 3, further comprising: (h) utilizingthe thermal profile of (g) to evaluate a malfunction in an existingapparatus.
 5. The method of claim 1, wherein the thermal device isselected from the group consisting of: a heater, thermoelectric cooler,heat sink, heat pipe, and combinations thereof.
 6. The method of claim1, wherein the apparatus is a manifold configured to transport amaterial that is a fluid.
 7. The method of claim 6, wherein the manifoldcomprises a plurality of components and wherein at least a portion ofthe plurality of components comprise one control zone.
 8. The method ofclaim 1, wherein Equation (1) is utilized in association with theinfluence matrix to obtain a linear thermal relationship, wherein theunknown thermal parameter for each thermal control zone is the heat fluxand the known first thermal parameter is a temperature value at thethermal controller for each thermal control zone, thereby determininghow much heat needs to come from a thermal device in a specific thermalcontrol zone to get a certain temperature at the thermal controller inthe same thermal control zone.
 9. The method of claim 1, wherein theinput value of (b) further corresponds to a thermal property of a nodeof the mesh defined in (c).
 10. The method of claim 1, wherein the inputvalue of (b) further corresponds to a thermal property of a thermalcontrol zone of the apparatus.
 11. A method comprising: (a) receiving amodel of an apparatus having a plurality of thermal control zones, eachthermal control zone of the apparatus comprising a thermal devicecontrolled by a thermal controller, wherein each thermal controller isconfigured to transmit, in response to a thermal parameter at a specificlocation within the apparatus, a control signal to the thermal device;(b) providing at least one input value that directly or indirectlycorresponds to at least one thermal property of at least one material ofthe apparatus; (c) defining a finite element analysis mesh having nodesfor the model of the apparatus; (d) applying at least one boundarycondition value to at least one portion of the model of the apparatus(e) determining the thermal correlation among at least a selectedplurality of the thermal control zones, comprising constructing an [n×n]influence matrix of matrix values, where n equals the number of selectedthermal control zones, by applying a known thermal parameter for eachcontrol zone within the influence matrix and conducting n simulations,wherein the constructing of the [n×n] influence matrix comprisingconducting n finite element analysis simulations of the apparatus basedon at least the finite element analysis mesh and the input value of (b)and the boundary condition value; and (f) using the influence matrix toobtain a result of the linear thermal relationship of an unknown thermalparameter for each control zone within the influence matrix
 12. Themethod of claim 11, wherein the thermal controller is within the samethermal control zone as the thermal device it is controlling.
 13. Themethod of claim 11, further comprising: (g) receiving at least one userinput that modifies the mesh defined in (c).
 14. The method of claim 11,further comprising: (g) applying the result obtained in (f) to the modelof (a) to obtain a thermal profile for the apparatus.
 15. The method ofclaim 14, further comprising: (h) utilizing the result obtained in (g)to evaluate a malfunction in an existing apparatus.
 16. The method ofclaim 14, further comprising: (h) utilizing the result obtained in (g)in designing a physical apparatus of the model received in (a).
 17. Themethod of claim 11, wherein the known thermal parameter for each thermalcontrol zone comprises the temperature at the thermal controller. 18.The method of claim 11, wherein the known thermal parameter for eachthermal control zone comprises the heat loss across a boundary of thecontrol zone.
 19. The method of claim 11, wherein Equation (1) isutilized in association with the influence matrix to obtain the linearthermal relationship, wherein the unknown thermal parameter for eachcontrol zone is the heat flux and the known thermal parameter is atemperature value at the thermal controller for each thermal controlzone, thereby determining how much heat needs to come from a heater in aspecific thermal control zone to get a certain temperature at thethermal controller in the same thermal control zone.
 20. The method ofclaim 11, wherein the apparatus is a manifold having a plurality ofchannels configured to transport a fluid.
 21. The method of claim 11,wherein the input value of (b) further corresponds to a thermal propertyof a node of the mesh defined in (c).
 22. A system comprising: acomputing device having a computer-readable medium configured to receivecomputer-executable instructions that when executed provide a model ofan apparatus having a plurality of thermal control zones, each thermalcontrol zone of the apparatus comprising a thermal device controlled bya thermal controller, wherein each thermal controller is configured totransmit, in response to a thermal parameter at a specific locationwithin the apparatus, a control signal to the thermal device; an inputdevice operatively coupled to the computing device configured to allowthe reception of at least one input regarding at least one material ofthe apparatus and an input relating to at least one boundary condition;a computer-readable medium having computer-readable instructions fordefining a mesh having nodes for the model of the apparatus; and acomputer-readable medium having computer-readable instructions that whenexecuted construct an [n×n] influence matrix, where n equals the numberof selected thermal control zones, each matrix value corresponding to avalue of a first thermal parameter selected from heat loss andtemperature for a corresponding one of the thermal control zones, theconstructing of the [n×n] influence matrix comprising conducting nfinite element analysis simulations of the apparatus based on the finiteelement analysis mesh, the input value of (b) and the boundary conditionvalue, each of the n finite element analysis simulations comprisingdetermining a matrix value of the first thermal parameter for eachthermal control zone by applying a value for the other thermal parameterselected from heat loss and temperature which is unknown-to eachboundary of a corresponding one of the thermal control zones and usingthe finite element analysis influence matrix to determine the value ofthe second thermal parameter for each control zone for a desired valueof the first of the first thermal parameter for each control zoneincluded in the selected plurality of thermal control zones.
 23. Thesystem of claim 22, further comprising: a computer-readable mediumhaving computer-readable instructions that when executed apply theresult of the linear thermal relationship to the model to obtain athermal profile for the apparatus.
 24. The system of claim 23, furthercomprising: a display adapter operatively coupled to the computingdevice for displaying the thermal profile of the apparatus.
 25. Thesystem of claim 23, further comprising: a computer-readable mediumhaving computer-readable instructions that when executed analyze thethermal profile of the apparatus to evaluate any malfunctions of aphysical apparatus having characteristics that are similar to the model.26. The method of claim 25, wherein the apparatus is a manifold having aplurality of channels configured to transport a fluid.
 27. The method ofclaim 26, wherein the apparatus is a manifold having a plurality ofchannels configured to transport a material that is a fluid at anelevated temperature and a solid at a lowered temperature.
 28. Thesystem of claim 23, further comprising: a computer-readable mediumhaving computer-readable instructions that when executed utilize thethermal profile of the apparatus in designing a physical apparatushaving characteristics that are similar to the model.
 29. The system ofclaim 23, wherein the known thermal parameter for each thermal controlzone comprises the temperature at the thermal controller.
 30. The methodof claim 23, wherein the computer-readable medium havingcomputer-readable instructions that when executed construct an [n×n]influence matrix comprises instructions for performing Equation (1) inassociation with the influence matrix to obtain a linear thermalrelationship, wherein the unknown thermal parameter for each thermalcontrol zone is the heat flux and the known first thermal parameter is atemperature value at the thermal controller for each thermal controlzone, thereby determining how much heat needs to come from a thermaldevice in a specific thermal control zone to get a certain temperatureat the thermal controller in the same thermal control zone.